The Knicks used the amnesty clause on Billups to create cap space needed to acquire Tyson Chandler.

Billups was under contract for $14.2 million. Under the terms of the amnesty rule, teams below the salary cap will now be permitted to bid for Billups' services. If no team claims him, Billups becomes an unrestricted free agent.

The Knicks replaced Billups at point guard with free agent Mike Bibby. They signed Bibby to a one-year deal for the veteran's minimum, ESPN The Magazine's Chris Broussard confirmed.

In a phone interview with ESPNNewYork.com's Ian O'Connor, Billups confirmed what his agent, Andy Miller, said Friday -- he would seriously consider quitting the game if a team he views as a non-contender claims him on waivers.

"If I get claimed by a team I don't want to play for, I would absolutely consider retirement," Billups said. "The game's been really good to me, and I don't want anyone to feel bad for me. I've made a lot of money, and I've saved most of it. I don't need the money now. I want to be able to play for something, a championship, and I want to be able to have my own destiny in my hands. If I don't, then retiring might have to be a decision I make."

Billups, a Colorado native, didn't want to leave Denver last February when he was shipped to New York in the Carmelo Anthony trade, and he didn't want to leave New York to clear room for Chandler. He made it clear Saturday he's tired of the dance. Long known in NBA circles as a dignified, team-first presence, Billups said he might need to change his approach.

"I'm not a selfish guy at all, never have been, but if I was a little more selfish maybe things would've been different for me," he said. "I've carried myself the way I was taught to, and in a lot of situations in my career I haven't been given the same respect.

"I've been underestimated at times and been taken advantage of in a lot of situations. I can go back 13, 14 years, where the fans, coaches, and everyone in the team offices love me and what I stand for, and yet I'm always the one who pays the price. I don't know of any player of my magnitude who's had the success I've had that has gone through what I've gone through, not one, whether they have the reputation I have or not. Nobody goes through these things.

"It's not in my makeup to be selfish. But it just feel like this time I need to be a little more concerned with me."

Billups averaged 16.8 points and 5.4 assists last season in Denver and New York.

Knicks interim general manager Glen Grunwald called the move part of "the nature of the business."

"We didn't want to get rid of Chauncey," Grunwald said. "When I talked to him today I told him, 'Chauncey it's not like we're waiving you because we don't want you. Look at it for what it is: We traded you basically for the starting center on the NBA championship team.'"

Billups embraced the idea that he could ultimately sign with a team that could meet the Knicks in the playoffs.

"I would like a chance at them, I'll tell you that much," he said. "I would absolutely love that."

In addition to having Bibby in the fold, coach Mike D'Antoni said the team would be comfortable using second-year guard Toney Douglas at the point. Rookie Iman Shumpert is also expected to play minutes at point guard.

D'Antoni believes that Anthony can facilitate the offense for long stretches.

"I think the team will look more like an old Celtics team, in the sense of going through Bird a lot, and they had two rangy shooters in the backcourt, [Danny] Ainge and Dennis Johnson," D'Antoni said. "It's just going to change in the sense that I had [Steve] Nash or somebody like that having the ball all the time. Now, Melo will be doing the pick-and-rolls more, and that's a good thing. Melo's one of the best passers we have, and he'll be involved in a lot more running the team.

The coach also commented on Bibby Saturday, before reports surfaced that the team had acquired him.

He was asked about Bibby's struggles in the postseason last year. Bibby shot 28 percent from the field and had an assist-to-turnover ratio of 23-to-17.

"You know, we'll see. I have a high level of confidence in him. He's a smart player. He can shoot the basketball and I think you know what you're going to get," D'Antoni said.

Asked if he was most interested in signing with the Miami Heat, a contender in need of a quarterback, Billups said, "I will re-evaluate my situation after these 48 hours of waivers. I want a chance to win, so any team that's playing for it all, I'd be interested in.

"I'm not 38. I'm still playing at a high level. I'm not interested in going somewhere to be a mentor coming off the bench."

Ian Begley is a regular contributor to ESPNNewYork.com. ESPNNewYork.com's Ian O'Connor contributed to this report.